112 Mr. Atwood's Propositions determining the Positions 
through the centre of gravity in a direction perpendicular to 
the former, and is called the shorter or transverse axe. A 
vertical plane drawn through the longer axe when the vessel 
floats upright divides it into two parts perfectly similar and 
equal ; in which particular the figures of ships may be termed 
regular ; although in other respects they are of forms not re- 
strained to any uniform proportions. From the equality of 
these two divisions of a vessel, it must necessarily happen that 
when it floats in a quiescent position the similar parts on the 
opposite sides will be equally elevated above the water's sur- 
face. A ship thus floating in a position of equilibrium may 
be conceived to be divided into two parts, by the horizontal 
plane which is coincident with the water's surface ; and the 
section formed by this plane passing through the body of the 
vessel is termed the principal section of the water, and is re- 
presented in fig. 2. as coincident with the line AB : when the 
ship is caused to heel, by being inclined round the longer axe 
through any angle SGK or NXB, (fig. 2.) the plane in the 
ship represented by the line AB will be transferred to the po- 
sition IN, and the section of the water will now pass through 
the vessel in the direction of a plane coincident with AP, in- 
clined to the former plane in the angle NXP, and may be 
termed, merely for the sake of distinction, the secondary sec- 
tion of the water. These two planes intersect each other in 
the line denoted by the point X, or rather in the line which 
is projected into the point X on the plane ABDH. Since the 
vessel is supposed to be inclined round the longer axe, it follows, 
that the line of intersection denoted by X will be parallel to 
that axis. And since from the laws of hydrostatics the volume 
PXN, which has been immersed in consequence of the incli- 
nation, is equal to the volume IXW, which has been elevated 
